The Bessel phase functions are used to represent the Bessel functions as a positive modulus and an oscillating trigonometric term. This decomposition can be used to aid root-finding of certain combinations of Bessel functions. In this article, we give some new properties of the modulus and phase functions and some asymptotic expansions derived from differential equation theory. We find a bound on the error of the first term of this asymptotic expansion and give a simple numerical method for refining this approximation via standard routines for the Bessel functions. We then show an application of the phase functions to the root finding problem for linear and cross-product combinations of Bessel functions. This method improves upon previous methods and allows the roots in ascending order of these functions to be calculated independently. We give some proofs of correctness and global convergence.

Item Type:	Refereed Article
Keywords:	Bessel phase functions
Research Division:	Mathematical Sciences
Research Group:	Pure Mathematics
Research Field:	Pure Mathematics not elsewhere classified
Objective Division:	Expanding Knowledge
Objective Group:	Expanding Knowledge
Objective Field:	Expanding Knowledge in the Mathematical Sciences
UTAS Author:	Horsley, DE (Mr David Horsley)
ID Code:	116803
Year Published:	2017 (online first 2016)
Web of Science® Times Cited:	1
Deposited By:	Mathematics and Physics
Deposited On:	2017-05-22
Last Modified:	2017-11-20
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